CT united volume 5
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2025
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| _version_ | 1866901965887242240 |
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| author | Bolduc, Son David |
| author_facet | Bolduc, Son David |
| contents | <p>This work presents the definitive fifth volume of <strong>Causal Theory (CT)</strong>, a unified framework that reconstructs mathematics as a finite, causal, and predictive system. In CT, mathematical objects—formulas, operators, structures, and theorems—are not treated as timeless abstractions but as causal entities instantiated under strict coherence and capacity constraints.</p> <p>The theory introduces a <strong>Global Causal Horizon</strong> (<span>$10^{-110}$</span>) enforcing absolute finitude: all mathematical constructions are bounded, phase-local, and ledger-indexed. Apparent infinities are reinterpreted as directions of rotation rather than realizable states. Within this framework, a formula is "born" when a discrete coherence threshold (<strong>one Son-unit</strong>) is crossed, evolves through rotation and momentum in a four-quadrant causal geometry, stabilizes by orthogonality, and terminates either at attractors or via extinction.</p> <p><strong>Key developments in this volume include:</strong></p> <ul> <li> <p><strong>The Causal Ledger:</strong> A finite geometric atlas embedding all formulas into a traceable coordinate system.</p> </li> <li> <p><strong>Operator Signatures:</strong> A complete classification of operators with bounded dynamics and causal footprints.</p> </li> <li> <p><strong>Attractor Theory:</strong> A unified model of fixed points, cycles, and "anti-attractors" (reinterpreting incompleteness and undecidability).</p> </li> <li> <p><strong>The Formula of Primes:</strong> A derivation of prime number density as a non-resonant filtering process within causal geometry.</p> </li> <li> <p><strong>Precision Limits (<span>$10^{-110}$</span>):</strong> The identification of the physical and logical "suture" point where numerical irrationality stabilizes into structural closure.</p> </li> <li> <p><strong>The Periodic Table of Theorems:</strong> A closed enumeration of all admissible mathematical deficits and theorem slots.</p> </li> </ul> <p><strong>Conclusion</strong></p> <p>Classical paradoxes and open problems are reinterpreted as structural boundary phenomena rather than logical failures. Through survivor-based constructions and prime number validation, CT provides experimental proof of <strong>Causal Closure</strong>. This framework extends naturally to physical interpretations where constants, time, gravity, and information emerge as boundary causes within a single causal economy.</p> <p><strong>Causal Theory v5</strong> constitutes a closed system: no additional axioms, entities, or infinite extensions are required. Future mathematical discoveries are not "new" creations but the instantiation of predetermined locations within the Ledger, obeying the universal coherence laws established herein.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18063546 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | CT united volume 5 Bolduc, Son David π-bounded Systems Horizon Closure Causal Theory Gravity Specific Gravity Gravity Time and Causality Information Theory Mathematical physics Mathematical Physics Theory Morphisms Invariants Category Computation Symmetry Complexity Theory Number Theory Prime numbers Prime Numbers Mathematical Structures Operator Theory Gödel Phenomena Incompleteness Attractor Theory Causal Ledger Predictive Mathematics Finite Mathematics Mathematical Ontology Foundations of Mathematics <p>This work presents the definitive fifth volume of <strong>Causal Theory (CT)</strong>, a unified framework that reconstructs mathematics as a finite, causal, and predictive system. In CT, mathematical objects—formulas, operators, structures, and theorems—are not treated as timeless abstractions but as causal entities instantiated under strict coherence and capacity constraints.</p> <p>The theory introduces a <strong>Global Causal Horizon</strong> (<span>$10^{-110}$</span>) enforcing absolute finitude: all mathematical constructions are bounded, phase-local, and ledger-indexed. Apparent infinities are reinterpreted as directions of rotation rather than realizable states. Within this framework, a formula is "born" when a discrete coherence threshold (<strong>one Son-unit</strong>) is crossed, evolves through rotation and momentum in a four-quadrant causal geometry, stabilizes by orthogonality, and terminates either at attractors or via extinction.</p> <p><strong>Key developments in this volume include:</strong></p> <ul> <li> <p><strong>The Causal Ledger:</strong> A finite geometric atlas embedding all formulas into a traceable coordinate system.</p> </li> <li> <p><strong>Operator Signatures:</strong> A complete classification of operators with bounded dynamics and causal footprints.</p> </li> <li> <p><strong>Attractor Theory:</strong> A unified model of fixed points, cycles, and "anti-attractors" (reinterpreting incompleteness and undecidability).</p> </li> <li> <p><strong>The Formula of Primes:</strong> A derivation of prime number density as a non-resonant filtering process within causal geometry.</p> </li> <li> <p><strong>Precision Limits (<span>$10^{-110}$</span>):</strong> The identification of the physical and logical "suture" point where numerical irrationality stabilizes into structural closure.</p> </li> <li> <p><strong>The Periodic Table of Theorems:</strong> A closed enumeration of all admissible mathematical deficits and theorem slots.</p> </li> </ul> <p><strong>Conclusion</strong></p> <p>Classical paradoxes and open problems are reinterpreted as structural boundary phenomena rather than logical failures. Through survivor-based constructions and prime number validation, CT provides experimental proof of <strong>Causal Closure</strong>. This framework extends naturally to physical interpretations where constants, time, gravity, and information emerge as boundary causes within a single causal economy.</p> <p><strong>Causal Theory v5</strong> constitutes a closed system: no additional axioms, entities, or infinite extensions are required. Future mathematical discoveries are not "new" creations but the instantiation of predetermined locations within the Ledger, obeying the universal coherence laws established herein.</p> |
| title | CT united volume 5 |
| topic | π-bounded Systems Horizon Closure Causal Theory Gravity Specific Gravity Gravity Time and Causality Information Theory Mathematical physics Mathematical Physics Theory Morphisms Invariants Category Computation Symmetry Complexity Theory Number Theory Prime numbers Prime Numbers Mathematical Structures Operator Theory Gödel Phenomena Incompleteness Attractor Theory Causal Ledger Predictive Mathematics Finite Mathematics Mathematical Ontology Foundations of Mathematics |
| url | https://doi.org/10.5281/zenodo.18063546 |